Exact Green Function for a Dirac Particle in Presence of Two Orthogonal Plane Wave Fields. Path Integral Derivation

2012 ◽  
Vol 51 (7) ◽  
pp. 2208-2219 ◽  
Author(s):  
H. K. Ould-Lahoucine ◽  
L. Chetouani
Keyword(s):  
Green Function ◽  
Plane Wave ◽  
Path Integral ◽  
Dirac Particle ◽  
Wave Fields ◽  
Orthogonal Plane

Green’s function for an electron model with a plane wave

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Hassen Ould Lahoucine ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Plane Wave ◽  
Path Integral ◽  
Equations Of Motion ◽  
Free Particle ◽  
Dirac Particle ◽  
Integral Approach ◽  
Electron Model ◽  
Plane Wave Field ◽  
The Green Function

AbstractThe Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.

scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

scholarly journals Dirac Particle in External Non-Abelian Gauge Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bilel Hamil ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Gauge Field ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Formalism ◽  
Abelian Gauge ◽  
Lorentz Gauge ◽  
Path Integral Formalism ◽  
The Green Function

The Green function of a Dirac particle in interaction with a non-Abelian SU(N) gauge field exactly and analytically determined via the path integral formalism by using the approach so-called “global projection.” The essential steps in the calculation are the choice of a convenient gauge (Lorentz gauge) and the introduction of two constraints, φ=kx (related to space) and Grassmannian η=kψ (related to Dirac matrices). Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived.

Path Integral for Dirac Particle in Plane Wave Field

2001 ◽  
Vol 64 (4) ◽  
pp. 285-291 ◽  
Author(s):  
S Zeggari ◽  
T Boudjedaa ◽  
L Chetouani
Keyword(s):  
Plane Wave ◽  
Wave Field ◽  
Path Integral ◽  
Dirac Particle ◽  
Plane Wave Field

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

ANOTHER DERIVATION OF A SUPERPARTICLE ACTION

1991 ◽  
Vol 06 (21) ◽  
pp. 1977-1982 ◽  
Author(s):  
E. S. FRADKIN ◽  
SH. M. SHVARTSMAN
Keyword(s):  
Green Function ◽  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation ◽  
Chiral Superfield

It is shown that the reparametrization invariant superparticle action can be determined by constructing the path-integral representation for the causal Green function of a chiral superfield interacting with an external Maxwell superfield.

Dynamical Theory for Simultaneous X-Ray Diffraction

1966 ◽  
Vol 10 ◽  
pp. 67-79
Author(s):  
P. Penning
Keyword(s):  
Experimental Data ◽  
Plane Wave ◽  
Quantitative Data ◽  
Reasonable Agreement ◽  
Dynamical Theory ◽  
Inversion Symmetry ◽  
Surprising Result ◽  
X Ray Diffraction ◽  
Wave Fields ◽  
X Ray

AbstractComplete dynamical solutions for three coupled plane-wave components in crystal structures with inversion symmetry have been found. After reviewing briefly the dynamical solutions for wave fields with two coupled plane-wave components, the results for the three-beam case are discussed in qualitative terms. Attention is paid to singular points and lines on the ω-surface, and to the attenuation of the mode-intensity because of absorption. The most surprising result is that in the case one of the reflections is forbidden (Umweganregung) the absorption is reduced in comparison with the adjoining two-beam cases. Experimental data are in reasonable agreement with the theory. Quantitative data are presented for a few three-beam cases of simultaneous diffraction of Cu Kα. radiation in germanium.

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